Begin by boiling a large pot of salted water. Add the uncooked penne rigate and cook according to package instructions until al dente. Drain the pasta and set it aside.
While the pasta is cooking, season the chicken breasts with kosher salt and black pepper. In a skillet over medium heat, cook the chicken for about 6-7 minutes per side, or until fully cooked and no longer pink in the center. Remove from the skillet and let it rest before slicing it into bite-sized pieces.
In the same skillet, add the all-purpose flour and cook for about a minute to remove the raw flavor. Gradually whisk in the sour cream (or Greek yogurt), cream cheese, and half and half (or whole milk). Stir until smooth and well combined.
Sprinkle the dry ranch mix into the creamy sauce and mix well. Then, add the spinach (if using frozen, make sure to thaw and squeeze out excess water first) and half of the shredded mozzarella cheese. Stir until everything is evenly combined and heated through.
Add the cooked penne rigate and sliced chicken to the skillet with the creamy sauce. Toss everything together until the pasta and chicken are fully coated in the cheesy goodness.
Preheat your oven to 350°F (175°C). Transfer the pasta mixture to a baking dish. Top with the remaining shredded mozzarella cheese. Bake for about 20 minutes, or until the cheese is bubbly and golden. Allow to cool slightly, then serve warm.